-LRB- CNN -RRB- -- Gunfire and shelling rang out across Syria 's coastal city of Latakia early Tuesday amid reports of Palestinian refugees fleeing a restive and impoverished enclave there .

At least five people died on Tuesday , according to a resident who requested anonymity for safety reasons , and the city remained under siege amid a military offensive against protesters .

The humanitarian situation deteriorated amid the government 's offensive in the city . Shops and bakeries were closed , and at least two mosques were damaged . The gunfire could be heard `` all night and morning , '' the witness said .

`` This is the fourth day that we do not have electricity or water . Landline phone connections have been down most of the day , '' he said by satellite phone .

Snipers perched atop various locations in the city 's al-Ramel neighborhood , the site of a Palestinian refugee camp , he said .

Demonstrations have taken place in the Ramel area every day since the Syrian uprising began five months ago , the Local Coordination Committees of Syria said .

The LCC , a network of opposition activists , said the area 's lack of basic urban services could be a reason why those in Ramel are angry at the Syrian government .

`` The tragedy of -LRB- Ramel -RRB- has not stopped since yesterday , '' the LCC said in a statement Tuesday .

The refugee camp normally holds 10,000 people , but reports have surfaced of many people fleeing violence there .

The resident said a large portion of the Ramel area has been evacuated .

The U.N. Relief and Works Agency , which provides assistance for Palestinian refugees across the Middle East , has expressed alarm over reports of heavy gunfire from Syrian security forces into the refugee camp and other areas .

`` Reports from various sources indicate deaths and casualties among the Palestinian refugee population , although poor communications make it impossible to confirm the exact number of dead and injured , '' it said in its latest statement .

Christopher Gunness , UNRWA spokesman , said refugees in Latakia had been asked to leave by the Syrian security forces . He said some left on their own because they were afraid for their lives .

`` We are asking the Syrian government for immediate access to the Palestinians , as their well-being is our responsibility , '' Gunness told CNN .

The state-run Syrian Arab News Agency said security forces entered the city only to protect its residents from armed gangs .

The Syrian government vehemently denied reports that more than 5,000 Palestinians fled the refugee camp in the area after it came under fire from Syrian security forces . It also reported Tuesday that reports of shelling by the navy on Ramel are `` completely untrue . ''

A video posted on YouTube Monday purportedly shows a dead girl who was shot in the eye as her father drove by a security checkpoint in Latakia .

Rami Abdul-Rahman of the Syrian Observatory for Human Rights , an activist group , said the girl and her parents were trying to flee in a car . The father was shot in the shoulder and the mother was lightly injured .

Bloodshed in the country has persisted since a government crackdown on anti-government protesters started in mid-March .

The LCC said at least 2,545 people have died . The vast majority were civilians , and 391 were security personnel , the LCC said .

The strong security reaction to demonstrators calling for political changes has spurred outrage among world powers , like the United States , and among Syria 's neighbors , such as Jordan and Turkey .

CNN can not independently verify opposition or government claims because Syria has restricted international journalists from reporting inside the country .

CNN 's Amir Ahmed , Arwa Damon , Nada Husseini and Yesim Comert contributed to this report .

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NEW : Resident : At least five people have died on Tuesday

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NEW : U.N. concerned over reports of security fire into Palestinian camp

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Syria 's government-run media denounces international reports as untrue

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More than 2,500 people have died since the uprising began , opposition activists say